Code
source("../_globals.r")DSAN 5100: Probabilistic Modeling and Statistical Computing
Section 03
source("../_globals.r")\[ \DeclareMathOperator*{\argmax}{argmax} \DeclareMathOperator*{\argmin}{argmin} \newcommand{\bigexp}[1]{\exp\mkern-4mu\left[ #1 \right]} \newcommand{\bigexpect}[1]{\mathbb{E}\mkern-4mu \left[ #1 \right]} \newcommand{\convergesAS}{\overset{\text{a.s.}}{\longrightarrow}} \newcommand{\definedas}{\overset{\text{def}}{=}} \newcommand{\definedalign}{\overset{\phantom{\text{def}}}{=}} \newcommand{\eqeventual}{\overset{\mathclap{\text{\small{eventually}}}}{=}} \newcommand{\Err}{\text{Err}} \newcommand{\expect}[1]{\mathbb{E}[#1]} \newcommand{\expectsq}[1]{\mathbb{E}^2[#1]} \newcommand{\fw}[1]{\texttt{#1}} \newcommand{\given}{\mid} \newcommand{\green}[1]{\color{green}{#1}} \newcommand{\heads}{\outcome{heads}} \newcommand{\iid}{\overset{\text{\small{iid}}}{\sim}} \newcommand{\lik}{\mathcal{L}} \newcommand{\loglik}{\ell} \newcommand{\mle}{\textsf{ML}} \newcommand{\nimplies}{\;\not\!\!\!\!\implies} \newcommand{\orange}[1]{\color{orange}{#1}} \newcommand{\outcome}[1]{\textsf{#1}} \newcommand{\param}[1]{{\color{purple} #1}} \newcommand{\pgsamplespace}{\{\green{1},\green{2},\green{3},\purp{4},\purp{5},\purp{6}\}} \newcommand{\prob}[1]{P\left( #1 \right)} \newcommand{\purp}[1]{\color{purple}{#1}} \newcommand{\spacecap}{\; \cap \;} \newcommand{\spacewedge}{\; \wedge \;} \newcommand{\tails}{\outcome{tails}} \newcommand{\Var}[1]{\text{Var}[#1]} \newcommand{\bigVar}[1]{\text{Var}\mkern-4mu \left[ #1 \right]} \]
Today’s Planned Schedule:
| Start | End | Topic | Recording | |
|---|---|---|---|---|
| Lecture | 12:30pm | 1:00pm | Markov Chains, Hidden Markov Models → | |
| 1:00pm | 1:30pm | PageRank → | ||
| 1:30pm | 2:00pm | Matrix Magic → | ||
| Break! | 2:00pm | 2:10pm | ||
| Lab | 2:10pm | 2:40pm | Lab → | |
| 2:40pm | 3:00pm | Student Presentation |
\[ \Pr(A \mid B) \definedas \frac{\Pr(A, B)}{\Pr(B)} \genfrac{}{}{0pt}{}{\leftarrow A\text{ and }B\text{ happen}}{\leftarrow \text{In world where }\Omega = B} \]
\[ P(\text{future} \mid \text{present}, {\color{orange}\text{past}}) = P(\text{future} \mid \text{present}) \]
Often stated in many different (confusing) ways, but think of anterograde amnesia: